Locally Regularized Sparse Graph by Fast Proximal Gradient Descent

• URL: http://arxiv.org/abs/2409.17090v1
• Date: Wed, 25 Sep 2024 16:57:47 GMT
• Title: Locally Regularized Sparse Graph by Fast Proximal Gradient Descent
• Authors: Dongfang Sun, Yingzhen Yang,
• Abstract summary: We propose a novel Regularized Sparse Graph abbreviated SRSG. Sparse graphs have been shown to be effective in clustering high-dimensional data. We show that SRSG is superior to other clustering methods.
• Score: 6.882546996728011
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Sparse graphs built by sparse representation has been demonstrated to be effective in clustering high-dimensional data. Albeit the compelling empirical performance, the vanilla sparse graph ignores the geometric information of the data by performing sparse representation for each datum separately. In order to obtain a sparse graph aligned with the local geometric structure of data, we propose a novel Support Regularized Sparse Graph, abbreviated as SRSG, for data clustering. SRSG encourages local smoothness on the neighborhoods of nearby data points by a well-defined support regularization term. We propose a fast proximal gradient descent method to solve the non-convex optimization problem of SRSG with the convergence matching the Nesterov's optimal convergence rate of first-order methods on smooth and convex objective function with Lipschitz continuous gradient. Extensive experimental results on various real data sets demonstrate the superiority of SRSG over other competing clustering methods.

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